Abstract

I will describe the votlage, megawatts, megavars (receieved and delivered), and power factor (lagging and leading) in terms of the electricity. Key goals are to understand substations and meters with regards to voltage and power factor as well as megawatts and megavars and to review the relatioship between power factor and voltage.

Introduction

Electric utilities collect meter readings in time intervals in various units. The intervals can be from 1 minute to 60 minute intervals collecing kW, kWh, VARh, volts. An utility needs to maintain a specified range for voltage across their electric network. When voltage is too low brown outs or electric motors may fail to work and when voltage is too high appliances and equiment can overheat, burn up, and possibly explode.

Power Factor

“A negative power factor (Lagging) occurs when the device (which is normally the load) generates power, which then flows back towards the source, which is normally considered the generator.”[1]

“In an electric power system, a load with a low power factor draws more current than a load with a high power factor for the same amount of useful power transferred. The higher currents increase the energy lost in the distribution system, and require larger wires and other equipment. Because of the costs of larger equipment and wasted energy, electrical utilities will usually charge a higher cost to industrial or commercial customers where there is a low power factor.” [1]

“Power factors below 1.0 require a utility to generate more than the minimum volt-amperes necessary to supply the real power (watts).
This increases generation and transmission costs. For example, if the load power factor were as low as 0.7, the apparent power would be 1.4 times the real power used by the load. Line current in the circuit would also be 1.4 times the current required at 1.0 power factor, so the losses in the circuit would be doubled.” [1] (since they are proportional to the square of the current).

“Alternatively all components of the system such as generators, conductors, transformers, and switchgear would be increased in size (and cost) to carry the extra current.” [1]

“Utilities typically charge additional costs to commercial customers who have a power factor below some limit, which is typically 0.9 to 0.95. Engineers are often interested in the power factor of a load as one of the factors that affect the efficiency of power transmission.” [1]

Definitions

Power factors are usually stated as “leading” or “lagging” to show the sign of the phase angle. Capacitive loads are leading (current leads voltage) and supply power, and inductive loads are lagging (current lags voltage) and consume power.

Univariate Plots Section

Voltage

Range of days: 2016-02-28, 2016-03-09

Summary of Voltage: 100.6, 120.8, 122.4, 122, 123.4, 130

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   100.6   120.8   122.4   122.0   123.4   130.0

Power Factor

MegaWatts, MVARs, and MVARS Squared

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   0.000   5.832   7.704   8.962  10.840  25.240

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
##  -3.572  -1.274  -0.754  -0.237   0.752   7.080     240

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
##   0.000   0.567   1.210   3.040   2.760  50.130     240

Univariate Analysis

What is the structure of your dataset?

Voltage Dataset

The voltage dataset contains endpoints collecting readings every 15 minutes.

## Classes 'grouped_df', 'tbl_df', 'tbl' and 'data.frame':  3031348 obs. of  10 variables:
##  $ substationName: chr  "HIGHLAND PARK" "DALLAS" "HIGHLAND PARK" "HOUSTON" ...
##  $ meter         : Factor w/ 2939 levels "200001","200002",..: 637 1979 38 1419 2335 2437 1806 346 2794 615 ...
##  $ readdate      : Factor w/ 1056 levels "2016-02-28 00:15:00",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ dtReadDate    : POSIXct, format: "2016-02-28" "2016-02-28" ...
##  $ dtReadDay     : POSIXct, format: "2016-02-28" "2016-02-28" ...
##  $ h             : num  0 0 0 0 0 0 0 0 0 0 ...
##  $ hm            : chr  "00:15" "00:15" "00:15" "00:15" ...
##  $ Voltage       : num  226 230 230 230 230 ...
##  $ VoltsHalf     : num  113 115 115 115 115 ...
##  $ voltage.bucket: Factor w/ 4 levels "(0,114]","(114,120]",..: 1 2 2 2 2 2 2 2 2 2 ...

Power Factor Dataset

The power factor dataset contains endpoints collecting readings every 60 minutes.

## Classes 'tbl_df', 'tbl' and 'data.frame':    3600 obs. of  16 variables:
##  $ substationName: chr  "ARLINGTON" "ARLINGTON" "ARLINGTON" "ARLINGTON" ...
##  $ ReadDate      : Factor w/ 240 levels "2016-02-28 00:10:00.000",..: 1 2 3 4 5 6 7 8 9 10 ...
##  $ dtReadDate    : POSIXct, format: "2016-02-28 00:10:00" "2016-02-28 01:10:00" ...
##  $ dtReadDay     : POSIXct, format: "2016-02-28" "2016-02-28" ...
##  $ h             : num  0 1 2 3 4 5 6 7 8 9 ...
##  $ mw            : num  8.8 8.75 8.92 9.17 9.55 ...
##  $ mvar.delivered: num  0.913 0.92 0.946 1.004 1.067 ...
##  $ mvar.received : num  0 0 0 0 0 ...
##  $ mvar          : num  0.913 0.92 0.946 1.004 1.067 ...
##  $ mwsquared     : num  77.5 76.5 79.5 84.1 91.3 ...
##  $ mvarsquared   : num  0.834 0.846 0.895 1.008 1.138 ...
##  $ va            : num  8.85 8.79 8.97 9.22 9.61 ...
##  $ pf            : num  0.995 0.995 0.994 0.994 0.994 ...
##  $ pfChart       : num  0.995 0.995 0.994 0.994 0.994 ...
##  $ desc          : Factor w/ 2 levels "Lagging","Leading": 1 1 1 1 1 1 2 2 2 2 ...
##  $ pf.range      : Factor w/ 7 levels "(0,0.88.]","(0.88,0.90]",..: 7 7 7 7 7 7 7 6 6 6 ...

Substation Dataset

Used for mapping the Voltage and Power Factor datasets together.

## 'data.frame':    27 obs. of  2 variables:
##  $ station       : Factor w/ 27 levels "BOYN","CHPH",..: 1 2 3 4 5 6 7 8 9 10 ...
##  $ substationName: Factor w/ 27 levels "Arlington","Austin",..: 4 9 5 17 11 24 6 26 10 15 ...

Structure of Voltage Data - uncleaned

## 'data.frame':    3033369 obs. of  4 variables:
##  $ readdate      : Factor w/ 1056 levels "2016-02-28 00:15:00",..: 1 2 3 4 5 6 7 8 9 10 ...
##  $ Voltage       : num  235 237 237 236 236 ...
##  $ substationName: Factor w/ 24 levels "Area 51","Arlington",..: 12 12 12 12 12 12 12 12 12 12 ...
##  $ meter         : int  300063 300063 300063 300063 300063 300063 300063 300063 300063 300063 ...

Structure of Power Factor - uncleaned

## 'data.frame':    10800 obs. of  4 variables:
##  $ ReadValue: num  0 0 0 0 0 0 0 0 0 0 ...
##  $ station  : Factor w/ 15 levels "BOYN","CHPH",..: 4 4 4 4 4 4 4 4 4 4 ...
##  $ name     : Factor w/ 3 levels "PMQD3D","PMQD3R",..: 1 1 1 1 1 1 1 1 1 1 ...
##  $ ReadDate : Factor w/ 240 levels "2016-02-28 00:10:00.000",..: 1 2 3 4 5 6 235 236 237 238 ...

What is/are the main feature(s) of interest in your dataset?

Voltage and Power Factor by time interval for each deliver point (substation) are the main features. One goal is to determine if we can predict power factor.

What other features in the dataset do you think will help support your

investigation into your feature(s) of interest? * mega watt
* mega var delivered
* mega var received

Did you create any new variables from existing variables in the dataset?

I created the power factor, mvars and the direction of the power factor (lagging and leading).

New variables where created for these datasets:

powerfactor_tidy and voltage_tidy

  • dtReadDate
  • dtReadDay
  • h
  • hm

voltage_tidy

  • voltage.bucket
  • VoltsHalf

powerfactor_tidy

  • mvars
  • mvarsquared
  • Power Factor
  • Power Factor Chart (Shifted Value)
  • desc - the direction of the power factor (Lagging vs Leading)

Of the features you investigated, were there any unusual distributions?

Austin and Dallas have bimodel distibutions of voltage for the days being reviewed.

The long leading tail on the voltage histogram, has a larger range in the data in the lower range than in the upper range.

Number of voltage intervals < 117: 43458
The range is : 100.6, 116.95

Number of voltage intervals > 126: 41439
The range is : 126.05, 129.95

Did you perform any operations on the data to tidy, adjust, or change the form of the data? If so, why did you do this?

Various methods were used to clean the data. For instance the ReadDates for the voltage intervals are in ending interval. The interval starts at 3/2/2016 00:15min and ends on 3/3/2016 00:00. To associate the 15 minute intervals with the correct hour and day, we had to roll back each 15 minute interval by 15 minutes.

The power factor data needed to be pivoted to get the data into a tidy format as well. The orignal data has the MegaWatt, MegaVars Delivered and Received in the same column, these values were split out into their own columns.

The substation names can have leading and trailing spaces so this data needed to be trimed.

Bivariate Plots Section

Voltage Plots

Box Plots

Scatter Plots

Dallas Substation Daily Voltage By Hour

The scatter plot shows the data along the time axis for the intervals for the day. The interesting point in this chart, which is similar to the histogram is how the shading changes from dark to grey, which is the points stacking on top of each other.

It takes 5 points on top of each other to make a solid point on this chart.
This demonstrates how the data is spread out over the ranges through the day by hour.

We can see there seems to be one metering point with high voltage which is consistently above the other voltage readings.

## [1] 0.8827947
Dallas Substation Meters

If we search all the meters on the Dallas substation, and sort descending by voltage we can obtain a list of meters with the highest voltage.

meter dtReadDay v.min v.mean v.median v.max v.intervals
300686 2016-03-06 126.15 127.5969 127.450 129.15 96
300686 2016-02-29 116.65 124.7021 124.675 129.00 96
300686 2016-03-09 112.65 120.2797 118.900 128.90 96

Voltage Descriptive Statistics
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   100.6   120.8   122.4   122.0   123.4   130.0
Standard Deviation
## [1] 2.047819
Range
## [1] 100.60 129.95
Quantiles
##     0%    25%    50%    75%   100% 
## 100.60 120.80 122.35 123.45 129.95

Mega Watts

Mega Watts Descriptive Statistics
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   0.000   5.832   7.704   8.962  10.840  25.240

MegaVAR

MegaVAR Descriptive Statistics
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
##  -3.572  -1.274  -0.754  -0.237   0.752   7.080     240

System Total MegaWatts, Mega VARs, MegaVars Squared

The multiple points are the 11 days we have in this dataset.

Power Factor Plots

Box Plots

Scatter Plots

Voltage.Min vs [MW, MVAR]

Voltage.Mean vs [MW, MVAR, Power Factor]

Voltage [Min, Mean, Median, Max] vs MW

Additional Substation Analysis

Substations meters where the voltage is less than nominal

Voltage Low Limit

Meters where more than 4 intervals below the 114 volts threshold.

Sample of Meters

Top Top 10 Substations Meter Counts for Low Voltage Meters

substationName meter dtReadDay count
HIGHLAND PARK 301146 2016-03-03 35
DALLAS 200227 2016-03-03 31
HIGHLAND PARK 301146 2016-02-28 28
AUSTIN 300964 2016-03-03 27
HIGHLAND PARK 300482 2016-03-03 27
HIGHLAND PARK 301146 2016-03-01 23
HIGHLAND PARK 301146 2016-03-07 23
HIGHLAND PARK 300482 2016-03-01 21
IRVING 301042 2016-03-05 21
CARROLTON 200811 2016-03-06 20

Voltage High Limit

Meters where more than 4 intervals below the 126 volts threshold.

Top Top 10 Substations Meter Counts for High Voltage Meters

substationName meter dtReadDay count
ARLINGTON 200277 2016-03-02 1
ARLINGTON 201979 2016-03-03 1
ARLINGTON 201979 2016-03-02 6
ARLINGTON 300872 2016-03-03 3
ARLINGTON 300872 2016-03-05 4
ARLINGTON 300872 2016-03-02 9
ARLINGTON 301334 2016-03-05 1
ARLINGTON 301334 2016-02-28 2
ARLINGTON 301796 2016-02-28 1
ARLINGTON 301796 2016-03-05 2

Bivariate Analysis

Talk about some of the relationships you observed in this part of the investigation. How did the feature(s) of interest vary with other features in the dataset?

Features of Interest

  • Voltage
  • By Substation
  • By Hour

  • Power Factor
  • By Substation
  • By Hour

Other Features

  • MW
  • MVAR

Did you observe any interesting relationships between the other features (not the main feature(s) of interest)?

This shows an interesting trend starting at 11AM (11:00 hours) until 10PM (20:00 hrs). The power factor spreads over a wider range. This is interesting on a system wide review, however we are more concerned with the power factor for each delivery point.

What was the strongest relationship you found?

The strongest relationship I found is between megawatts and power factor.
As the megawatts increases the power factor approaches the 1, for each of the Substations for this single day investigation.

Multivariate Plots Section

Correlation Analysis

Coefficient, r

Strength of Association Positive Negative
Small .1 to .3 -0.1 to -0.3
Medium .3 to .5 -0.3 to -0.5
Large .5 to 1.0 -0.5 to -1.0

Correlation Matrix

Review the correlation between power factor and voltage using Pearsons.

Correlation Plots Power Factor

Correlation Plots Power Factor Shifted Value

Correlation of Voltage & Power Factor

Review the correlation between power factor and voltage using Pearsons.

## 
##  Pearson's product-moment correlation
## 
## data:  summary_total$v.mean and summary_total$pf
## t = -3.7994, df = 3104, p-value = 0.0001478
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.10296188 -0.03294618
## sample estimates:
##        cor 
## -0.0680378

Voltage vs PF with Linear Model

MegaWatt vs PF with Linear Model by Substation

Power Factor Shifted Value (Lagging and Leading)

Power Factor Ratio Plot

Voltage Scatter Plots With Bucket (Cut)

Voltage Bucket Summary

Counts of the voltage instances in each bucketed range.

##   (0,114] (114,120] (120,126] (126,140] 
##      1958    520655   2467296     41439
Voltage Bucket Data By Day
dtReadDay substationName (0,114] (114,120] (120,126] (126,140] total p1 p2 p3 p4
2016-02-28 AREA 51 NA 164 4634 NA NA NA NA NA NA
2016-02-28 ARLINGTON 1 738 9526 3 10268 0.0097390 7.1873783 92.77367 0.0292170
2016-02-28 AUSTIN 16 9227 4289 NA NA NA NA NA NA
2016-02-28 CARROLTON NA 967 7864 NA NA NA NA NA NA
2016-02-28 DALLAS 35 12337 6815 6 19193 0.1823582 64.2786433 35.50774 0.0312614
2016-02-28 EULESS NA 160 7230 1 NA NA NA NA NA
2016-02-28 FORNEY NA 212 8131 111 NA NA NA NA NA
2016-02-28 FT WORTH NA 934 14332 92 NA NA NA NA NA
2016-02-28 GARLAND NA 504 16940 24 NA NA NA NA NA
2016-02-28 HIGHLAND PARK 143 15510 9972 NA NA NA NA NA NA
2016-02-28 HILLSBORO NA 48 8014 NA NA NA NA NA NA
2016-02-28 HOUSTON 33 11579 6144 NA NA NA NA NA NA
2016-02-28 IRVING 7 3833 35505 5 39350 0.0177891 9.7407878 90.22872 0.0127065
2016-02-28 MESQUITE 7 1026 9332 NA NA NA NA NA NA
2016-02-28 MILFORD NA 74 2609 3 NA NA NA NA NA
2016-02-28 MINERAL WELLS NA 175 2068 60 NA NA NA NA NA
2016-02-28 RICHARDSON NA 1599 14423 10 NA NA NA NA NA
2016-02-28 ROCKWALL NA 147 1067 226 NA NA NA NA NA
2016-02-28 ROWLET 2 800 18576 584 19962 0.0100190 4.0076145 93.05681 2.9255586
2016-02-28 TEMPLE 2 686 1808 NA NA NA NA NA NA
2016-02-28 UPTOWN NA 2 1564 2562 NA NA NA NA NA
2016-02-28 VICTORIA 1 225 2736 590 3552 0.0281532 6.3344595 77.02703 16.6103604
2016-02-28 WACO NA 957 6816 NA NA NA NA NA NA
2016-02-28 WAXAHACHIE NA 68 3675 NA NA NA NA NA NA
2016-02-29 AREA 51 NA 56 4741 NA NA NA NA NA NA
2016-02-29 ARLINGTON NA 265 10003 NA NA NA NA NA NA
2016-02-29 AUSTIN NA 487 12948 NA NA NA NA NA NA
2016-02-29 CARROLTON NA 382 8449 NA NA NA NA NA NA
2016-02-29 DALLAS 3 939 18382 160 19484 0.0153972 4.8193389 94.34408 0.8211866
2016-02-29 EULESS NA 81 7307 NA NA NA NA NA NA
2016-02-29 FORNEY NA 75 8370 98 NA NA NA NA NA
2016-02-29 FT WORTH NA 482 15055 72 NA NA NA NA NA
2016-02-29 GARLAND 11 324 17231 NA NA NA NA NA NA
2016-02-29 HIGHLAND PARK 1 1092 24683 NA NA NA NA NA NA
2016-02-29 HILLSBORO NA 11 8051 NA NA NA NA NA NA
2016-02-29 HOUSTON NA 623 17127 NA NA NA NA NA NA
2016-02-29 IRVING 3 2447 37055 NA NA NA NA NA NA
2016-02-29 MESQUITE 7 504 9853 NA NA NA NA NA NA
2016-02-29 MILFORD NA 102 2586 NA NA NA NA NA NA
2016-02-29 MINERAL WELLS NA 31 2221 51 NA NA NA NA NA
2016-02-29 RICHARDSON 2 846 15180 NA NA NA NA NA NA
2016-02-29 ROCKWALL NA 66 1175 236 NA NA NA NA NA
2016-02-29 ROWLET 1 355 19641 NA NA NA NA NA NA
2016-02-29 TEMPLE NA 481 2014 NA NA NA NA NA NA
2016-02-29 UPTOWN NA 1 1224 2993 NA NA NA NA NA
2016-02-29 VICTORIA NA 107 2772 673 NA NA NA NA NA
2016-02-29 WACO NA 714 6964 NA NA NA NA NA NA
2016-02-29 WAXAHACHIE NA 87 3656 NA NA NA NA NA NA
2016-03-01 AREA 51 NA 93 4698 NA NA NA NA NA NA
2016-03-01 ARLINGTON 8 675 9646 NA NA NA NA NA NA
2016-03-01 AUSTIN 19 9973 3541 NA NA NA NA NA NA
2016-03-01 CARROLTON NA 943 7887 NA NA NA NA NA NA
2016-03-01 DALLAS 56 14637 4764 6 19463 0.2877254 75.2042337 24.47721 0.0308277
2016-03-01 EULESS NA 117 7464 3 NA NA NA NA NA
2016-03-01 FORNEY NA 139 8360 32 NA NA NA NA NA
2016-03-01 FT WORTH 2 753 14799 79 15633 0.0127934 4.8167338 94.66513 0.5053413
2016-03-01 GARLAND NA 477 17087 1 NA NA NA NA NA
2016-03-01 HIGHLAND PARK 164 20193 5456 NA NA NA NA NA NA
2016-03-01 HILLSBORO NA 45 8016 NA NA NA NA NA NA
2016-03-01 HOUSTON 33 13977 3838 NA NA NA NA NA NA
2016-03-01 IRVING 5 4657 34956 NA NA NA NA NA NA
2016-03-01 MESQUITE 10 991 9439 NA NA NA NA NA NA
2016-03-01 MILFORD NA 121 2567 NA NA NA NA NA NA
2016-03-01 MINERAL WELLS NA 192 2102 8 NA NA NA NA NA
2016-03-01 RICHARDSON 5 1849 14176 NA NA NA NA NA NA
2016-03-01 ROCKWALL NA 121 1294 120 NA NA NA NA NA
2016-03-01 ROWLET 1 1191 19150 NA NA NA NA NA NA
2016-03-01 TEMPLE NA 539 1861 NA NA NA NA NA NA
2016-03-01 UPTOWN NA 4 1813 2500 NA NA NA NA NA
2016-03-01 VICTORIA 2 335 2840 375 3552 0.0563063 9.4313063 79.95495 10.5574324
2016-03-01 WACO NA 1061 6705 NA NA NA NA NA NA
2016-03-01 WAXAHACHIE NA 102 3642 NA NA NA NA NA NA
2016-03-02 AREA 51 NA 368 4428 NA NA NA NA NA NA
2016-03-02 ARLINGTON 3 947 9489 16 10455 0.0286944 9.0578670 90.76040 0.1530368
2016-03-02 AUSTIN 5 1888 11640 NA NA NA NA NA NA
2016-03-02 CARROLTON 3 1991 7111 NA NA NA NA NA NA
2016-03-02 DALLAS 6 2088 17228 141 19463 0.0308277 10.7280481 88.51667 0.7244515
2016-03-02 EULESS NA 202 7365 17 NA NA NA NA NA
2016-03-02 FORNEY NA 366 8198 71 NA NA NA NA NA
2016-03-02 FT WORTH 10 1383 15258 82 16733 0.0597621 8.2651049 91.18508 0.4900496
2016-03-02 GARLAND 2 698 16866 35 17601 0.0113630 3.9656838 95.82410 0.1988523
2016-03-02 HIGHLAND PARK 13 2618 23283 NA NA NA NA NA NA
2016-03-02 HILLSBORO NA 110 7953 1 NA NA NA NA NA
2016-03-02 HOUSTON 3 2283 15654 6 17946 0.0167168 12.7214978 87.22835 0.0334336
2016-03-02 IRVING 16 6261 33723 56 40056 0.0399441 15.6306171 84.18963 0.1398043
2016-03-02 MESQUITE 27 1987 8449 NA NA NA NA NA NA
2016-03-02 MILFORD 1 271 2510 2 2784 0.0359195 9.7341954 90.15805 0.0718391
2016-03-02 MINERAL WELLS NA 400 1903 1 NA NA NA NA NA
2016-03-02 RICHARDSON 16 3274 12834 1 16125 0.0992248 20.3038760 79.59070 0.0062016
2016-03-02 ROCKWALL NA 294 1199 43 NA NA NA NA NA
2016-03-02 ROWLET 34 4805 15508 NA NA NA NA NA NA
2016-03-02 TEMPLE 3 938 1458 NA NA NA NA NA NA
2016-03-02 UPTOWN NA 18 2889 1412 NA NA NA NA NA
2016-03-02 VICTORIA 4 722 2618 304 3648 0.1096491 19.7916667 71.76535 8.3333333
2016-03-02 WACO 6 2120 5689 NA NA NA NA NA NA
2016-03-02 WAXAHACHIE NA 149 3594 NA NA NA NA NA NA
2016-03-03 AREA 51 NA 273 4620 NA NA NA NA NA NA
2016-03-03 ARLINGTON NA 739 9716 4 NA NA NA NA NA
2016-03-03 AUSTIN 49 8224 5260 NA NA NA NA NA NA
2016-03-03 CARROLTON 1 1797 7319 NA NA NA NA NA NA
2016-03-03 DALLAS 81 12596 6512 5 19194 0.4220069 65.6246744 33.92727 0.0260498
2016-03-03 EULESS NA 83 7485 16 NA NA NA NA NA
2016-03-03 FORNEY NA 353 8251 33 NA NA NA NA NA
2016-03-03 FT WORTH 2 1294 15591 94 16981 0.0117779 7.6202815 91.81438 0.5535599
2016-03-03 GARLAND NA 574 17003 119 NA NA NA NA NA
2016-03-03 HIGHLAND PARK 181 16480 9251 NA NA NA NA NA NA
2016-03-03 HILLSBORO NA 50 8011 NA NA NA NA NA NA
2016-03-03 HOUSTON 39 10545 7268 NA NA NA NA NA NA
2016-03-03 IRVING 11 5830 34367 NA NA NA NA NA NA
2016-03-03 MESQUITE 21 1864 8578 NA NA NA NA NA NA
2016-03-03 MILFORD NA 272 2410 4 NA NA NA NA NA
2016-03-03 MINERAL WELLS NA 396 1908 NA NA NA NA NA NA
2016-03-03 RICHARDSON 8 2804 13408 NA NA NA NA NA NA
2016-03-03 ROCKWALL NA 273 1256 7 NA NA NA NA NA
2016-03-03 ROWLET 23 4193 16128 NA NA NA NA NA NA
2016-03-03 TEMPLE 3 1411 1082 NA NA NA NA NA NA
2016-03-03 UPTOWN NA 3 2716 1598 NA NA NA NA NA
2016-03-03 VICTORIA NA 460 3167 21 NA NA NA NA NA
2016-03-03 WACO 1 1480 6292 NA NA NA NA NA NA
2016-03-03 WAXAHACHIE NA 117 3627 NA NA NA NA NA NA
2016-03-04 AREA 51 NA 343 4550 NA NA NA NA NA NA
2016-03-04 ARLINGTON 3 933 9525 NA NA NA NA NA NA
2016-03-04 AUSTIN 1 1126 12308 NA NA NA NA NA NA
2016-03-04 CARROLTON NA 1453 7664 NA NA NA NA NA NA
2016-03-04 DALLAS 11 1735 17450 95 19291 0.0570214 8.9938313 90.45669 0.4924576
2016-03-04 EULESS NA 212 7368 3 NA NA NA NA NA
2016-03-04 FORNEY NA 328 8121 88 NA NA NA NA NA
2016-03-04 FT WORTH 2 1484 15516 79 17081 0.0117089 8.6880159 90.83777 0.4625022
2016-03-04 GARLAND 3 744 16758 17 17522 0.0171213 4.2460906 95.63977 0.0970209
2016-03-04 HIGHLAND PARK 1 2656 23285 NA NA NA NA NA NA
2016-03-04 HILLSBORO NA 39 8022 NA NA NA NA NA NA
2016-03-04 HOUSTON NA 1624 16229 NA NA NA NA NA NA
2016-03-04 IRVING 10 6349 34140 NA NA NA NA NA NA
2016-03-04 MESQUITE 13 1774 8578 NA NA NA NA NA NA
2016-03-04 MILFORD NA 240 2443 4 NA NA NA NA NA
2016-03-04 MINERAL WELLS NA 319 1807 82 NA NA NA NA NA
2016-03-04 RICHARDSON 7 2602 13324 1 15934 0.0439312 16.3298607 83.61993 0.0062759
2016-03-04 ROCKWALL NA 205 1245 85 NA NA NA NA NA
2016-03-04 ROWLET 9 2889 17361 NA NA NA NA NA NA
2016-03-04 TEMPLE NA 1069 1426 NA NA NA NA NA NA
2016-03-04 UPTOWN NA 4 2225 2089 NA NA NA NA NA
2016-03-04 VICTORIA NA 413 2694 445 NA NA NA NA NA
2016-03-04 WACO 3 1583 6148 NA NA NA NA NA NA
2016-03-04 WAXAHACHIE NA 95 3648 NA NA NA NA NA NA
2016-03-05 AREA 51 NA 299 4595 NA NA NA NA NA NA
2016-03-05 ARLINGTON 3 818 9632 7 10460 0.0286807 7.8202677 92.08413 0.0669216
2016-03-05 AUSTIN 47 8564 4824 NA NA NA NA NA NA
2016-03-05 CARROLTON 14 1577 7529 NA NA NA NA NA NA
2016-03-05 DALLAS 54 13628 5797 5 19484 0.2771505 69.9445699 29.75262 0.0256621
2016-03-05 EULESS NA 174 7408 1 NA NA NA NA NA
2016-03-05 FORNEY NA 260 8107 170 NA NA NA NA NA
2016-03-05 FT WORTH NA 1054 15922 88 NA NA NA NA NA
2016-03-05 GARLAND NA 661 16739 68 NA NA NA NA NA
2016-03-05 HIGHLAND PARK 88 15378 10541 NA NA NA NA NA NA
2016-03-05 HILLSBORO NA 77 7985 1 NA NA NA NA NA
2016-03-05 HOUSTON 18 10935 6611 NA NA NA NA NA NA
2016-03-05 IRVING 26 5275 35169 31 40501 0.0641959 13.0243698 86.83489 0.0765413
2016-03-05 MESQUITE 30 1470 8865 NA NA NA NA NA NA
2016-03-05 MILFORD NA 188 2493 6 NA NA NA NA NA
2016-03-05 MINERAL WELLS NA 268 1912 28 NA NA NA NA NA
2016-03-05 RICHARDSON 6 2403 13519 5 15933 0.0376577 15.0819055 84.84906 0.0313814
2016-03-05 ROCKWALL 2 201 1191 141 1535 0.1302932 13.0944625 77.58958 9.1856678
2016-03-05 ROWLET 15 1733 18489 108 20345 0.0737282 8.5180634 90.87737 0.5308430
2016-03-05 TEMPLE 1 637 1761 NA NA NA NA NA NA
2016-03-05 UPTOWN NA 31 1685 2603 NA NA NA NA NA
2016-03-05 VICTORIA NA 438 2581 533 NA NA NA NA NA
2016-03-05 WACO NA 1377 6490 NA NA NA NA NA NA
2016-03-05 WAXAHACHIE NA 83 3660 NA NA NA NA NA NA
2016-03-06 AREA 51 NA 144 4749 NA NA NA NA NA NA
2016-03-06 ARLINGTON 1 848 9611 NA NA NA NA NA NA
2016-03-06 AUSTIN 9 1100 12422 NA NA NA NA NA NA
2016-03-06 CARROLTON 24 1268 7827 NA NA NA NA NA NA
2016-03-06 DALLAS 2 1461 17881 238 19582 0.0102135 7.4609335 91.31345 1.2154019
2016-03-06 EULESS NA 219 7365 NA NA NA NA NA NA
2016-03-06 FORNEY NA 267 8415 53 NA NA NA NA NA
2016-03-06 FT WORTH NA 1192 15819 74 NA NA NA NA NA
2016-03-06 GARLAND NA 665 17176 11 NA NA NA NA NA
2016-03-06 HIGHLAND PARK 3 2310 23692 NA NA NA NA NA NA
2016-03-06 HILLSBORO NA 51 8108 NA NA NA NA NA NA
2016-03-06 HOUSTON 1 1282 16278 NA NA NA NA NA NA
2016-03-06 IRVING 16 4775 36190 2 40983 0.0390406 11.6511724 88.30491 0.0048801
2016-03-06 MESQUITE 22 1465 8975 NA NA NA NA NA NA
2016-03-06 MILFORD NA 199 2489 NA NA NA NA NA NA
2016-03-06 MINERAL WELLS NA 208 2094 1 NA NA NA NA NA
2016-03-06 RICHARDSON 6 2160 14047 5 16218 0.0369959 13.3185350 86.61364 0.0308299
2016-03-06 ROCKWALL NA 162 1233 141 NA NA NA NA NA
2016-03-06 ROWLET 6 1329 19104 NA NA NA NA NA NA
2016-03-06 TEMPLE 1 636 1763 NA NA NA NA NA NA
2016-03-06 UPTOWN NA 1 1586 2729 NA NA NA NA NA
2016-03-06 VICTORIA NA 382 3003 167 NA NA NA NA NA
2016-03-06 WACO NA 1359 6607 NA NA NA NA NA NA
2016-03-06 WAXAHACHIE NA 59 3684 NA NA NA NA NA NA
2016-03-07 AREA 51 NA 89 4807 NA NA NA NA NA NA
2016-03-07 ARLINGTON NA 430 10128 NA NA NA NA NA NA
2016-03-07 AUSTIN 21 11206 2308 NA NA NA NA NA NA
2016-03-07 CARROLTON 2 774 8343 NA NA NA NA NA NA
2016-03-07 DALLAS 34 14498 4852 5 19389 0.1753572 74.7743566 25.02450 0.0257878
2016-03-07 EULESS NA 63 7615 NA NA NA NA NA NA
2016-03-07 FORNEY NA 147 8512 77 NA NA NA NA NA
2016-03-07 FT WORTH NA 538 16630 81 NA NA NA NA NA
2016-03-07 GARLAND 6 362 17579 NA NA NA NA NA NA
2016-03-07 HIGHLAND PARK 99 19063 6846 NA NA NA NA NA NA
2016-03-07 HILLSBORO NA 14 8145 NA NA NA NA NA NA
2016-03-07 HOUSTON 19 15394 2438 NA NA NA NA NA NA
2016-03-07 IRVING 13 4272 36735 NA NA NA NA NA NA
2016-03-07 MESQUITE 7 792 9757 NA NA NA NA NA NA
2016-03-07 MILFORD NA 168 2519 1 NA NA NA NA NA
2016-03-07 MINERAL WELLS NA 87 2021 195 NA NA NA NA NA
2016-03-07 RICHARDSON 1 1061 15159 NA NA NA NA NA NA
2016-03-07 ROCKWALL NA 73 1210 253 NA NA NA NA NA
2016-03-07 ROWLET 1 546 19898 NA NA NA NA NA NA
2016-03-07 TEMPLE NA 552 1944 NA NA NA NA NA NA
2016-03-07 UPTOWN NA 4 1203 3112 NA NA NA NA NA
2016-03-07 VICTORIA NA 200 2426 926 NA NA NA NA NA
2016-03-07 WACO NA 725 7241 NA NA NA NA NA NA
2016-03-07 WAXAHACHIE NA 62 3682 NA NA NA NA NA NA
2016-03-08 AREA 51 NA 30 4865 NA NA NA NA NA NA
2016-03-08 ARLINGTON NA 195 10359 NA NA NA NA NA NA
2016-03-08 AUSTIN NA 586 12948 NA NA NA NA NA NA
2016-03-08 CARROLTON 3 380 9023 NA NA NA NA NA NA
2016-03-08 DALLAS 2 1104 18310 69 19485 0.0102643 5.6658968 93.96972 0.3541186
2016-03-08 EULESS NA 75 7604 NA NA NA NA NA NA
2016-03-08 FORNEY NA 62 8753 135 NA NA NA NA NA
2016-03-08 FT WORTH 16 556 17285 87 17944 0.0891663 3.0985288 96.32746 0.4848417
2016-03-08 GARLAND 6 247 17722 3 17978 0.0333741 1.3739014 98.57604 0.0166871
2016-03-08 HIGHLAND PARK 1 846 25257 NA NA NA NA NA NA
2016-03-08 HILLSBORO 1 20 8138 NA NA NA NA NA NA
2016-03-08 HOUSTON NA 571 17090 NA NA NA NA NA NA
2016-03-08 IRVING 3 2656 38606 NA NA NA NA NA NA
2016-03-08 MESQUITE 6 420 10129 NA NA NA NA NA NA
2016-03-08 MILFORD 1 115 2666 2 2784 0.0359195 4.1307471 95.76149 0.0718391
2016-03-08 MINERAL WELLS NA 35 2140 174 NA NA NA NA NA
2016-03-08 RICHARDSON 1 751 15467 NA NA NA NA NA NA
2016-03-08 ROCKWALL NA 64 1111 361 NA NA NA NA NA
2016-03-08 ROWLET NA 270 20171 NA NA NA NA NA NA
2016-03-08 TEMPLE NA 384 2112 NA NA NA NA NA NA
2016-03-08 UPTOWN NA NA 570 3747 NA NA NA NA NA
2016-03-08 VICTORIA NA 76 2584 890 NA NA NA NA NA
2016-03-08 WACO NA 353 7612 NA NA NA NA NA NA
2016-03-08 WAXAHACHIE NA 65 3678 NA NA NA NA NA NA
2016-03-09 AREA 51 NA 43 4882 NA NA NA NA NA NA
2016-03-09 ARLINGTON NA 134 10421 NA NA NA NA NA NA
2016-03-09 AUSTIN 18 10184 3331 NA NA NA NA NA NA
2016-03-09 CARROLTON 2 267 9383 NA NA NA NA NA NA
2016-03-09 DALLAS 17 13134 6297 27 19475 0.0872914 67.4403081 32.33376 0.1386393
2016-03-09 EULESS NA 86 7594 NA NA NA NA NA NA
2016-03-09 FORNEY NA 34 8899 221 NA NA NA NA NA
2016-03-09 FT WORTH 1 474 17823 82 18380 0.0054407 2.5788901 96.96953 0.4461371
2016-03-09 GARLAND 13 77 17945 5 18040 0.0720621 0.4268293 99.47339 0.0277162
2016-03-09 HIGHLAND PARK 35 22963 3201 NA NA NA NA NA NA
2016-03-09 HILLSBORO NA 10 8148 NA NA NA NA NA NA
2016-03-09 HOUSTON 9 13316 4330 NA NA NA NA NA NA
2016-03-09 IRVING 4 2065 39286 NA NA NA NA NA NA
2016-03-09 MESQUITE 3 220 10237 NA NA NA NA NA NA
2016-03-09 MILFORD NA 125 2772 3 NA NA NA NA NA
2016-03-09 MINERAL WELLS NA 15 2211 172 NA NA NA NA NA
2016-03-09 RICHARDSON 3 417 15803 NA NA NA NA NA NA
2016-03-09 ROCKWALL NA 53 1134 348 NA NA NA NA NA
2016-03-09 ROWLET NA 263 20083 NA NA NA NA NA NA
2016-03-09 TEMPLE NA 235 2165 NA NA NA NA NA NA
2016-03-09 UPTOWN NA NA 437 3879 NA NA NA NA NA
2016-03-09 VICTORIA NA 77 2896 607 NA NA NA NA NA
2016-03-09 WACO NA 105 7766 NA NA NA NA NA NA
2016-03-09 WAXAHACHIE NA 80 3664 NA NA NA NA NA NA

Counts of the voltage instances in each bucketed range by hour by substations

##   (0,114] (114,120] (120,126] (126,140] 
##      1958    520655   2467296     41439

Create a line graph of voltages vs. h so that each voltage.bucket is a line tracking the median user voltage counts across hour.

Compare Voltage and Power Factor Range Counts

##  substationName                        ReadDate  
##  Length:240         2016-02-28 00:10:00.000:  1  
##  Class :character   2016-02-28 01:10:00.000:  1  
##  Mode  :character   2016-02-28 02:10:00.000:  1  
##                     2016-02-28 03:10:00.000:  1  
##                     2016-02-28 04:10:00.000:  1  
##                     2016-02-28 05:10:00.000:  1  
##                     (Other)                :234  
##    dtReadDate                    dtReadDay                  
##  Min.   :2016-02-28 00:10:00   Min.   :2016-02-28 00:00:00  
##  1st Qu.:2016-03-01 11:55:00   1st Qu.:2016-03-01 00:00:00  
##  Median :2016-03-03 23:40:00   Median :2016-03-03 12:00:00  
##  Mean   :2016-03-03 23:40:00   Mean   :2016-03-03 12:00:00  
##  3rd Qu.:2016-03-06 11:25:00   3rd Qu.:2016-03-06 00:00:00  
##  Max.   :2016-03-08 23:10:00   Max.   :2016-03-08 00:00:00  
##                                                             
##        h               mw         mvar.delivered    mvar.received  
##  Min.   : 0.00   Min.   : 0.000   Min.   :0.00000   Min.   :0.000  
##  1st Qu.: 5.75   1st Qu.: 6.369   1st Qu.:0.00000   1st Qu.:1.059  
##  Median :11.50   Median : 8.251   Median :0.00000   Median :1.492  
##  Mean   :11.50   Mean   : 8.514   Mean   :0.01423   Mean   :1.526  
##  3rd Qu.:17.25   3rd Qu.:10.579   3rd Qu.:0.00000   3rd Qu.:2.084  
##  Max.   :23.00   Max.   :14.602   Max.   :0.69300   Max.   :2.416  
##                                                                    
##       mvar          mwsquared       mvarsquared          va        
##  Min.   :-2.416   Min.   :  0.00   Min.   :0.000   Min.   : 0.000  
##  1st Qu.:-2.084   1st Qu.: 40.56   1st Qu.:1.121   1st Qu.: 6.725  
##  Median :-1.492   Median : 68.07   Median :2.226   Median : 8.456  
##  Mean   :-1.511   Mean   : 78.78   Mean   :2.728   Mean   : 8.706  
##  3rd Qu.:-1.059   3rd Qu.:111.92   3rd Qu.:4.343   3rd Qu.:10.601  
##  Max.   : 0.693   Max.   :213.22   Max.   :5.837   Max.   :14.627  
##                                                                    
##        pf            pfChart            desc            pf.range  
##  Min.   :0.8934   Min.   :0.9986   Lagging:  5   (0.98,1]   :123  
##  1st Qu.:0.9616   1st Qu.:1.0052   Leading:235   (0.96,0.98]: 59  
##  Median :0.9814   Median :1.0186                 (0.92,0.94]: 22  
##  Mean   :0.9723   Mean   :1.0277                 (0.94,0.96]: 19  
##  3rd Qu.:0.9948   3rd Qu.:1.0384                 (0.90,0.92]: 13  
##  Max.   :1.0000   Max.   :1.1066                 (Other)    :  3  
##  NA's   :1        NA's   :1                      NA's       :  1

This chart demonstrates how the voltage can vary on the lower and upper ends of the voltage ranges.

Multivariate Analysis

Talk about some of the relationships you observed in this part of the

investigation. Were there features that strengthened each other in terms of looking at your feature(s) of interest?

  • MegaWatt vs Power Factor (GOOD)
  • Voltage vs Power Factor (NOTHING)
  • Voltage vs PF with Linear Model - Facet Substation (NOTHING)
  • MegaWatt vs PF with Linear Model by Substation (GOOD)
  • Power Factor Shifted Value (Lagging and Leading) By Hour (GOOD), FINAL CHART
  • Power Factor Ratio Plot (GOOD)

Were there any interesting or surprising interactions between features?

Voltage Scatter Plots With Bucket and Power Factor

The voltage and power factor for the entire system seem to track or follow a similar trend here. They have similar shapes. Or at least when the power factor range increases the voltage drops less in the system. This could be for many reasons.

Models

One idea to be explored is if we can predict when the power factor will go below 0.98 lagging or leading. This could help us change the system parameters to keep the network in operating efficiency. ## Goals * Create model for each substation to predict when power factor goes below 0.98 based on the hourly readings. If we can predict at a minimum 2 hours ahead this would be idea. The initial

## 
## Calls:
## m1: lm(formula = pf ~ I(sqrt(mw)), data = powerfactor_tidy)
## m2: lm(formula = pf ~ I(sqrt(mw)) + mw, data = powerfactor_tidy)
## m3: lm(formula = pf ~ I(sqrt(mw)) + mvar, data = powerfactor_tidy)
## m4: lm(formula = pf ~ I(sqrt(mw)) + mw + h, data = powerfactor_tidy)
## m5: lm(formula = pf ~ I(sqrt(mw)) + mvar + desc, data = powerfactor_tidy)
## 
## ================================================================================
##                             m1         m2         m3         m4         m5      
## --------------------------------------------------------------------------------
##   (Intercept)             0.955***   0.864***   0.967***   0.871***   0.970***  
##                          (0.002)    (0.005)    (0.002)    (0.005)    (0.002)    
##   I(sqrt(mw))             0.009***   0.072***   0.005***   0.071***   0.006***  
##                          (0.001)    (0.004)    (0.001)    (0.004)    (0.001)    
##   mw                                -0.010***             -0.010***             
##                                     (0.001)               (0.001)               
##   mvar                                          0.003***              0.001     
##                                                (0.000)               (0.000)    
##   h                                                       -0.000***             
##                                                           (0.000)               
##   desc: Leading/Lagging                                              -0.008***  
##                                                                      (0.001)    
## --------------------------------------------------------------------------------
##   R-squared                   0.1        0.2        0.1        0.2        0.1   
##   adj. R-squared              0.1        0.1        0.1        0.2        0.1   
##   sigma                       0.0        0.0        0.0        0.0        0.0   
##   F                         254.5      295.1      184.0      235.5      139.9   
##   p                           0.0        0.0        0.0        0.0        0.0   
##   Log-likelihood           8257.4     8406.7     8309.4     8455.5     8332.7   
##   Deviance                    1.4        1.3        1.4        1.2        1.3   
##   AIC                    -16508.8   -16805.3   -16610.8   -16901.0   -16655.3   
##   BIC                    -16490.5   -16780.9   -16586.3   -16870.4   -16624.7   
##   N                        3345       3345       3345       3345       3345     
## ================================================================================

Linear Model Test

Expected Result : 0.9903636

##         fit       lwr      upr
## 1 0.9935461 0.9542009 1.032891

Summary

## 
## Call:
## lm(formula = pf ~ I(sqrt(mw)) + mvar + desc, data = powerfactor_tidy)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.110210 -0.007643  0.006219  0.013327  0.029249 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.9700961  0.0020414 475.208  < 2e-16 ***
## I(sqrt(mw))  0.0055247  0.0006944   7.956 2.40e-15 ***
## mvar         0.0005560  0.0003866   1.438     0.15    
## descLeading -0.0083754  0.0012239  -6.843 9.18e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.02005 on 3341 degrees of freedom
##   (255 observations deleted due to missingness)
## Multiple R-squared:  0.1116, Adjusted R-squared:  0.1108 
## F-statistic: 139.9 on 3 and 3341 DF,  p-value: < 2.2e-16

Anova

## Analysis of Variance Table
## 
## Response: pf
##               Df  Sum Sq  Mean Sq F value    Pr(>F)    
## I(sqrt(mw))    1 0.10698 0.106981 266.065 < 2.2e-16 ***
## mvar           1 0.04300 0.042998 106.937 < 2.2e-16 ***
## desc           1 0.01883 0.018829  46.829 9.178e-12 ***
## Residuals   3341 1.34338 0.000402                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual Plots

Discuss the strengths and limitations of your model.

Final Plots and Summary

Are the final three plots varied and do they meet some of the following criteria:
1 Draw comparisons.
2 Identify trends.
3 Engage a wide audience.
4 Explain a complicated finding.
5 Clarify a gap between perception and reality.
6 Enable the reader to digest large amounts of information.

Each plot reveals an important and different comparison or trend in the data. The plots incorporate many of the variables from the data set in a way that allows the plots to convey a lot of information while still being interpreted easily. The plots fulfill 4 or more of the criteria.

Plot One

Voltage and Power Factor Outlier plot helps the user to quickly identify which substations are out the bounded region.

This chart represents the voltage and power factor for all data points collected for 2016-03-02. The chart allows one to see how much of the data falls out of the voltage and power factor defined region (0.98 (left) to 0.99 (right), and 114v to 126v).

We can see we have more points with Lagging power factors outside the required range for efficient power factor values.

NEED 4 or more…

1 Draw comparisons. * YES - Comparisons between substations 2 Identify trends.
* NO - Trends - Nope, need multiple days… or day without VVar day with VVar 3 Engage a wide audience. * Yes, easy to review… 4 Explain a complicated finding.
* YES - which substations behaved and what where their min and max for pf and voltages 5 Clarify a gap between perception and reality.
* MAYBE - If a person looks at the current momentary… status * the daily status might be different 6 Enable the reader to digest large amounts of information. * YES - Power Factor, Voltage, Ranges, inside the comfort zone,

Plot Two

Heatmap of Voltage to help user to see how all substations performed during each 15 minute period during the day. One chart helps to see who is in the red (low) or in the purple (high) voltage ranges.

1 Draw comparisons.
2 Identify trends.
3 Engage a wide audience.
4 Explain a complicated finding.
5 Clarify a gap between perception and reality.
6 Enable the reader to digest large amounts of information.

Plot Three

Description goes here please… Note, I think I have a better plot to put here, this one kinda goes along with Plot_One, it is just another form of the plot.

Total

Reflection

I was interested in finding substations where the voltage has high varience and to see what affect this has on the power factor. When reviewing this data day to day variations are affected by the voltage requlators to help reduce the voltage on the transmission lines. A voltage load profile with less varience should have a better power factor (what does better mean, 0.98-1, lagging or leading?[2]

Identify which days have VVC (Volt Var Contol On). 3/2 off 3/3 On — Walter Has these notes.

The section explains any important decisions in the analysis and how those decisions affected the analysis.

Need to make sure to handle cases when data is missing from a day over a few date ranges.

Automate additional processes.

Voltage

Voltage seems to be normally like distributed by the hour through out the day and by substation for the entire by hour. This seems good since large flucuations in voltage are bad for consumers and commercial businesses.

Power Factor can flucuation from lagging to leading in on substation in a single day. This requires more effort to control the voltage , watts, and vars across the power lines. Can I show that when voltage is tightly controled we have less variability in the power factor??????

TODO: Find a sub with the best range in voltage and look at its power factor. Then compare it’s MW and MVARS to all other substations.

The section reflects on how the analysis was conducted and reports on the struggles and successes throughout the analysis. The section provides at least one idea or question for future work.

The section provides a rich and well-written reflection of * struggles * Date Formatting without lubridate was one mistake or line of code which would not run. * Exploring for relationships - In industry standards it is typically regarded as controling voltage with less varience helps keep the power factor with in nominal ranges. When looking for the correlation between power factor and votlage we really can not see one most likely because the voltage is in a narrow range, and power factor is more affected by kw and mvars since it is a ratio of real / active power.

  • successes
    • MegaWatt vs MegaVar
    • MegaWatt vs Power Factor
    • Drilling down from Substation to Meter to find the bad meters
  • Lessons learned Electricity is a pain to review.

The section poses ideas or questions for future work. * multiple days would be benficial * months to months * 12 month analysis of trends * seasonal trends * collect more power factor data down to 15min intervals * examining the varience of all the load shapes for each variable. * revewing the load shape for all meters on every substation.

Equations

Ohm’s Law

We monitor voltage since a utility can change the voltage across the power lines. Keeping the system balanced at low voltages between 114 and 126 helps to improve the efficeny of the power transmission since lower voltages mean less resistance.

I = Current
R = Resistance
V = Voltage

\(V = I*R\)

\(R = \frac{V}{I}\)

\(I = \frac{V}{R}\)

Calculate watts from Voltage

P(kW) = PF × I(A) × V(V) / 1000

Power - kW, kiloWatts
Power Factor
I - Amps
Voltage - Volts

3 Phase
P(kW) = √3 × PF × I(A) × VL-L(V) / 1000

Power Factor

P, Real Power - kW -> PMWD3D (MW) Real power is kilowatts, in the initial dataset this is represented as PMWD3D.

S, Apparent Power (volt amperess) We will be solving for apparent power.

Q, Reactive Power Reactive power is kVAR, in the initial dataset PMQD3D is Delivered and
PMQR3D is Received. The total kVars are (PMQD3D-PMQR3D).

The Power Triangle Equation

See Reference for explanation

\(S^2 = P^2 + Q^2\)

\(S=\sqrt{P^2 + Q^2}\)

Power Factor

The power factor is defined as the ratio of real power to apparent power.

\[Power Factor=\frac{P}{\sqrt{P^2 + Q^2}}\]

\[Power Factor =\frac{kW}{\sqrt{kW^2 + (kVAR Delieverd - kVAR Received)^2}}\]

Leading and Lagging Power Factor

  • Delivered VARs - Received VARs > 0 Lagging
  • Delivered VARs - Received VARs < 0 Leading

References

[1] https://en.wikipedia.org/wiki/Power_factor [2] https://en.wikipedia.org/wiki/Distribution_management_system#Volt-VAR_Control_.28VVC.29 https://en.wikipedia.org/wiki/Ohm%27s_law
https://en.wikipedia.org/wiki/Volt-ampere_reactive
http://www.statpower.net/Content/310/R%20Stuff/SampleMarkdown.html
http://rmarkdown.rstudio.com/authoring_basics.html
http://www.ats.ucla.edu/stat/r/library/contrast_coding.htm
http://vita.had.co.nz/papers/tidy-data.pdf http://adv-r.had.co.nz/Style.html

https://www.rstudio.com/wp-content/uploads/2015/02/data-wrangling-cheatsheet.pdf https://www.rstudio.com/wp-content/uploads/2015/02/rmarkdown-cheatsheet.pdf http://www.r-statistics.com/2012/03/do-more-with-dates-and-times-in-r-with-lubridate-1-1-0/ http://www.statmethods.net/management/aggregate.html http://yihui.name/knitr/options/ http://tutorials.iq.harvard.edu/R/Rgraphics/Rgraphics.html http://kbroman.org/knitr_knutshell/pages/Rmarkdown.html http://data.princeton.edu/R/linearModels.html https://statistics.laerd.com/statistical-guides/pearson-correlation-coefficient-statistical-guide.php